We have it, west coast of scotland (wet), and a small shaded north facing garden and a dog. We tried for 6-7 years to get the grass going even before we got the dog and it was still muddy swamp. When ds came along it was just unusable for 80% of the year.
So it was either fake grass or slab/chip. We did a mixture of all three, avoiding straight lines where possible and the fake grass which takes up around 1/3 of the space adds a good balance with colour, shape and texture.
It was brillant for us, suddenly gave us loads of usable space, great for ds when he was young as he could go out straight away all year round when there was a break in the rain and kick a ball.
We discouraged ddog from peeing on the grass after it was laid and he now pees on the chips only so I don't know if dog pee is a problem. When we bought the grass from the builders merchants they recommended short grass for dogs and picking up poo is very easy. We don't have problems with it being too hot (scotland is rarely too hot!)
Of course it is naff compared to a nice lawn, but in some gardens it is an excellent alternative to chips and slabs alone.
Do be aware once it has been down a few years it is a bit of work to maintain as leaf debris etc builds up in it and moss develops. At least twice a year it needs moss killer down and a good brush out to remove some of the dead moss (and keep the dog off it for a few days while the moss killer down). It is quite physical work to do, so we are glad we only have a small area.